Question

The City Housing Authority has received 75 applications from qualified applicants for eight low-income apartments. Three of the apartments are on the north side of town, and five are on the south side of town.

(a) If the apartments are to be assigned by means of a lottery, what is the probability that a specific qualified applicant will be selected for one of these apartments?

Answer 1

Probability of selection on first draw = 1/75
Probability of selection on second draw =1/74
Probability of selection on third draw = 1/73
and so on until
Probability of selection on eighth draw =1/68
Probability of secified applicant being selected is
1/75 * 1/74 * 1/73 * 1/72 * 1/71 * 1/70 * 1/69 * 1/68

Answer 2

specified*

Answer 3

that is a huge number

Answer 4

Not so. It is a very small number. Try multiplying just the first two fractions:
\[\frac{1}{75}\times \frac{1}{74}=0.00018\]

Answer 5

Sorry, my bad. The events being selected on the first draw, or the second draw and so on for a specific applicant are mutually exclusive. Therefore the probabilities must be added:
\[\frac{1}{75}+\frac{1}{74}+\frac{1}{73}+\frac{1}{72}+\frac{1}{71}+\frac{1}{70}+\frac{1}{69}+\frac{1}{68}\]